A supervoxel-based segmentation method for prostate MR images

Transcription

1 A supervoxel-based segmentation method for prostate MR images Zhiqiang Tian, Emory University Lizhi Liu, Emory University Baowei Fei, Emory University Proceedings Title: MEDICAL IMAGING 2015: IMAGE PROCESSING Conference Name: Conference on Medical Imaging - Image Processing Publisher: SPIE-INT SOC OPTICAL ENGINEERING Conference Place: Orlando, FL Volume/Issue: Volume 9413 Publication Date: Type of Work: Conference Post-print: After Peer Review Publisher DOI: / Permanent URL: Final published version: Copyright information: 2015 SPIE. Accessed July 3, :42 PM EDT

2 A supervoxel-based segmentation method for prostate MR images Zhiqiang Tian 1, LiZhi Liu 1, and Baowei Fei 1,2,* 1 Department of Radiology and Imaging Sciences, Emory University, Atlanta, GA 2 Department of Biomedical Engineering, Emory University and Georgia Institute of Technology Abstract Accurate segmentation of the prostate has many applications in prostate cancer diagnosis and therapy. In this paper, we propose a Supervoxel based method for prostate segmentation. The prostate segmentation problem is considered as assigning a label to each supervoxel. An energy function with data and smoothness terms is used to model the labeling process. The data term estimates the likelihood of a supervoxel belongs to the prostate according to a shape feature. The geometric relationship between two neighboring supervoxels is used to construct a smoothness term. A three-dimensional (3D) graph cut method is used to minimize the energy function in order to segment the prostate. A 3D level set is then used to get a smooth surface based on the output of the graph cut. The performance of the proposed segmentation algorithm was evaluated with respect to the manual segmentation ground truth. The experimental results on 12 prostate volumes showed that the proposed algorithm yields a mean Dice similarity coefficient of 86.9%±3.2%. The segmentation method can be used not only for the prostate but also for other organs. Keywords HHS Public Access Author manuscript Published in final edited form as: Proc SPIE Int Soc Opt Eng March 20; 9413:. doi: / Magnetic resonance imaging (MRI); prostate cancer; segmentation; supervoxel; 3D graph cut; 3D level set 1. INTRODUCTION It is estimated that there are 233,000 new cases of prostate cancer and 29,480 deaths from prostate cancer in the USA in 2014 [1]. Magnetic resonance imaging (MRI) has been increasingly used for the detection and diagnosis of prostate cancer [2 8]. Prostate delineation on MRI images helps physicians to measure the prostate size and help for treatment planning. However, prostate segmentation is a non-trivial because of the similar MR intensities between the prostate and adjacent tissue and because of the MR intensity inhomogeneity in the prostate region. Moreover, the prostate has a wide variety of shape appearance among different patients. There are extensive studies [3, 9 14] in delineating the prostate surface from MRI. Qiu et al. [3] proposed a global optimization-based approach to segment T2 weighted MRI by * Corresponding author: bfei@emory.edu; Website:

3 Tian et al. Page 2 2. METHODS 2.1 Supervoxel enforcing the geometrically axial symmetry of the prostate shapes. This method coherently segmented a series of 2-D slices. Toth [9] presented a novel multi-feature landmark-free active appearance model for segmenting 2-D medical images. These methods yield good results but cannot handle medical images in a 3D manner. Egger [12] proposed an automated segmentation algorithm by applying a 3D graph-based algorithm for prostate segmentation. This method had a high computational cost due to their pixel-based manner. To resolve these problems, we propose a supervoxel-based 3D graph cuts method for segmenting the prostate. We cluster groups of similar pixels into supervoxels, which are used to compute robust local statistics. This supervoxel-based method reduces the computational and memory costs without sacrificing accuracy because supervoxels naturally respect the object surface. The output of the graph cuts is used as an initialization for 3D level set based segmentation [15, 16], which can produce smooth prostate surfaces. An overview of the proposed method is shown in Fig. 1. Given a 3D MR volume, supervoxels are first generated by an efficient algorithm as described below. This is the key step for the proposed method. Supervoxel is the basic processing unit of our method, which reduces the computational and memory cost significantly. Secondly, the initial segmentation is obtained by minimizing the supervoxel-based energy function using a 3D graph cut algorithm. Finally, a 3D level set algorithm is adopted to smooth the prostate surface of the initial segmentation. The initial segmentation is close to the true surface, so it makes the level set converge quickly. We consider one MR slice as a 2D image. Superpixel is a set of adjacent pixels in a slice with similar intensity or/and texture, while Supervoxel is a set of superpixels with similar intensity in the 3D volume. Fig. 2 demonstrates the supervoxels and their geometric relationships. An intersection between a supervoxel SV i and Slice j is a superpixel defined as: (1). Supervoxel is where M is the number of the supervoxels in an MRI volume, SV i is the lifespan of the superpvoxel SV i. The j-th superpixel of SV i is, which consists of a set of pixels in one slice. Note that, different supervoxels may have different beginnings, endings, and different lifespans. In this work, supervoxels are obtained by using a simple linear iterative clustering method (SLIC) [17]. 2.2 Energy function based on supervoxels Graph cut [18] has been improved to be an efficient method [12] for segmenting 3D medical images. We consider prostate segmentation as a supervoxel labeling problem in a 3D graph.

4 Tian et al. Page 3 The superpvoxels are labeled as the prostate or background by optimizing an energy function. The energy function is defined as: where l is the label of the supervoxel, Label 1 represents the prostate, while Label 0 corresponds to the background, N SV SV is a neighborhood. We assume that N contains a supervoxel pair {SV p, SV q } which has a common boundary in one slice at least. The data term D SV (l SV ) quantifies the distance of each supervoxel to a proposed shape model. The smoothness term V SV p, SVq (l SVp, l SVq ) quantifies how likely two supervoxels have the same label. The parameter γ balances the weight between the data term and the smoothness term. In this work, a shape model is proposed to build the data term. Three key slices are selected as the initialization, which are selected from the apex, base, and middle of the prostate. Four to six points are marked for each key slice. Based on these initializations, two semiellipsoids are fitted. One is toward to the apex, the other is toward to the base. Note that these two fitted surfaces of semi-ellipsoids are not accurate. They are just used to compute the shape data term. Once the fitted surfaces are obtained, the prostate and the background shape data term can be defined as: where S sv represents the mean value of shape feature of a supervoxel. f is defined as: where d is the distance of a pixel to the fitted surfaces. k and β are shape feature parameters which control the fatness and slope of the shape. The affinities of each pair of neighboring supervoxels SV p and SV q are used to compute the smoothness term. The supervoxels that are close to each other and have more common slices will be grouped together. Based on this principle, the smoothness term is defines as: where SV p SV q stands for the number of common slices between two neighboring supervoxels. SV p and SV q are the number of slices (lifespan) of supervoxel SV p and SV q, respectively. This geometry based smoothness term encourages supervoxels that have similar locations and share more common slices to be assigned as the same label. Once data term and smootheness term are obtained, the energy function can be minimized by the graph cut algorithm. Each supervoxel will be assigned a binary label. The pixels in (3) (4) (5) (2) (6)

5 Tian et al. Page D level set 2.4 Evaluation metrics 3. RESULTS 3.1 MR images the same supervoxel have the same label. Then the prostate surface can be derived from the labeled volume data. The supervoxel-based graph cut algorithm is an efficient method. However, the output may be not satisfactory when the supervoxel fails to find the boundary of the prostate accurately. To solve this problem, the prostate surface obtained from the graph cut should be refined. 3D level set is adopted in our method to refine the prostate surface. As the surface is good enough for the initialization of the level set algorithm, only several iterations are needed to achieve convergence. Four evaluation metrics are used to evaluate the performance, which are DICE similarity coefficient (DSC), relative volume difference (RVD), Hausdorff distance (HD), and average surface distance (ASD) [3, 19]. The DSC is calculated by: where V gt is the number of voxels in the segmentation of the ground truth and V alg is the number of voxels in the segmentation of the proposed algorithm. The RVD is computed as: The RVD is used to evaluate whether the algorithm tends to over-segment or under-segment the prostate. To compute the HD and ASD, a distance from a voxel x to a surface Y is defined firstly as d(x, Y) = min y Y x y. The HD between two surfaces X and Y is calculated by: The ASD is defined as: where X and Y represent the number of voxels in the surface X and Y, respectively. The proposed method was evaluated on our prostate MR data set, which consists of 12 T2- weighted volumes. Transverse images were used in the experiments. The voxel sizes of the volumes are from 0.625mm to 1mm. The field of view varies from mm 2 to mm 2. (7) (8) (9) (10)

6 Tian et al. Page Qualitative evaluation results The performance of the proposed method is evaluated qualitatively by visual comparison with the manually segmented contours. Meanwhile, the demonstration of the supervoxels is showed in Fig. 3. The qualitative results from 12 prostate volumes are shown in Fig. 4. Blue curves are manual segmented ground truth by an experienced radiologist, while the red curves are output of the proposed method. Our method has satisfactory results for all the 12 volumes. 3.3 Quantitative evaluation results 4. CONCLUSIONS Acknowledgments References The quantitative results are shown in Table 1. We proposed a supervoxel-based method to segment the prostate from 3D MR images. The experiments on our MRI data set showed that this method could extract the prostate surface accurately. To the best of our knowledge, this is the first study to use supervoxel for the segmentation of prostate MR images. It reduces the computational and memory cost significantly. Meanwhile, the proposed method makes the graph cuts algorithm to be competent for handling big 3D medical data. The segmentation method can be applied to various applications in prostate imaging. This research is supported in part by NIH grants R21CA176684, R01CA and P50CA128301, Georgia Cancer Coalition Distinguished Clinicians and Scientists Award, and the Center for Systems Imaging (CSI) of Emory University School of Medicine. 1. Siegel R, Ma J, Zou Z, Jemal A. Cancer statistics, CA: a cancer journal for clinicians. 2014; 64(1):9 29. [PubMed: ] 2. Toth R, Tiwari P, Rosen M, Reed G, Kurhanewicz J, Kalyanpur A, Pungavkar S, Madabhushi A. A magnetic resonance spectroscopy driven initialization scheme for active shape model based prostate segmentation. Med Image Anal. 2011; 15(2): [PubMed: ] 3. Wu Qiu JY, Ukwatta Eranga, Sun Yue, Rajchl Martin, Fenster Aaron. Prostate Segmentation: An Efficient Convex Optimization Approach With Axial Symmetry Using 3-D TRUS and MR Images. IEEE Transactions on Medical Imaging. 2014; 33(4): [PubMed: ] 4. Fei B, Duerk JL, Boll DT, Lewin JS, Wilson DL. Slice-to-volume registration and its potential application to interventional MRI-guided radiofrequency thermal ablation of prostate cancer. IEEE Trans Med Imaging. 2003; 22(4): [PubMed: ] 5. Fei B, Lee Z, Boll DT, Duerk JL, Lewin JS, Wilson DL. Image registration and fusion for interventional MRI guided thermal ablation of the prostate cancer. MICCAI. 2003: Litjens G, Debats O, Barentsz J, Karssemeijer N, Huisman H. Computer-aided detection of prostate cancer in MRI. IEEE transactions on medical imaging. 2014; 33(5): [PubMed: ] 7. Johnson LM, Turkbey B, Figg WD, Choyke PL. Multiparametric MRI in prostate cancer management. Nature Reviews Clinical Oncology. 2014; 11(6): Qiu W, Yuan J, Ukwatta E, Sun Y, Rajchl M, Fenster A. Dual optimization based prostate zonal segmentation in 3D MR images. Medical image analysis. 2014; 18(4): [PubMed: ]

7 Tian et al. Page 6 9. Toth R, Madabhushi A. Multifeature Landmark-Free Active Appearance Models: Application to Prostate MRI Segmentation. IEEE Transactions on Medical Imaging. 2012; 31(8): [PubMed: ] 10. Litjens G, Toth R, van de Ven W, Hoeks C, Kerkstra S, van Ginneken B, Vincent G, Guillard G, Birbeck N, Zhang J, Strand R, Malmberg F, Ou Y, Davatzikos C, Kirschner M, Jung F, Yuan J, Qiu W, Gao Q, Edwards PE, Maan B, van der Heijden F, Ghose S, Mitra J, Dowling J, Barratt D, Huisman H, Madabhushi A. Evaluation of prostate segmentation algorithms for MRI: The PROMISE12 challenge. Med Image Anal. 2014; 18(2): [PubMed: ] 11. Guo Y, Gao Y, Shao Y, Price T, Oto A, Shen D. Deformable segmentation of 3D MR prostate images via distributed discriminative dictionary and ensemble learning. Medical physics. 2014; 41(7): [PubMed: ] 12. Egger J. PCG-Cut: Graph Driven Segmentation of the Prostate Central Gland. Plos One. 2013; 8(10): Ou Y, Doshi J, Erus G, Davatzikos C. Multi-atlas segmentation of the prostate: A zooming process with robust registration and atlas selection. Medical Image Computing and Computer Assisted Intervention (MICCAI) Grand Challenge: Prostate MR Image Segmentation. 2012; 7: Mahapatra D, Buhmann JM. Prostate MRI segmentation using learned semantic knowledge and graph cuts. Biomedical Engineering, IEEE Transactions on. 2014; 61(3): Chan TF, Vese LA. Active contours without edges. IEEE transactions on Image processing. 2001; 10(2): [PubMed: ] 16. Zhang Y, Matuszewski BJ, Shark L, Moore CJ. Medical image segmentation using new hybrid level-set method. 2008: Achanta R, Shaji A, Smith K, Lucchi A, Fua P, Susstrunk S. SLIC superpixels compared to stateof-the-art superpixel methods. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2012; 34(11): [PubMed: ] 18. Boykov Y, Veksler O, Zabih R. Fast approximate energy minimization via graph cuts. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2001; 23(11): Garnier C, Bellanger JJ, Wu K, Shu HZ, Costet N, Mathieu R, de Crevoisier R, Coatrieux JL. Prostate Segmentation in HIFU Therapy. IEEE Transactions on Medical Imaging. 2011; 30(3): [PubMed: ]

8 Tian et al. Page 7 Figure 1. The framework of the proposed method.

9 Tian et al. Page 8 Figure 2. Supervoxels and their geometric relations in the 3D medical image volume.

10 Tian et al. Page 9 Figure 3. Qualitative evaluation results of the proposed method. The first row is one slice from a typical MR volume, while the second row is the adjacent slice of the same volume. The first column is the original slice. The second column is the supervoxel demonstration. Same color between two slices means the same supervoxel. The blue supervoxels are the segmented prostate obtained from the graph cut. In the third column, the blue boundaries of supervoxels that belong to the prostate are superposed on the original slices to demonstrate the good adherence of the superpvoxel to the boundaries of the prostate. The red curves in the fourth column are the final segmentation obtained by using the 3D level set method. The blue curves are the manual segmented ground truth.

11 Tian et al. Page 10 Figure 4. Qualitative results of the proposed method.

12 Tian et al. Page 11 Table 1 Quantitative evaluation of the supervoxel-based prostate segmentation method V01 V02 V03 V04 V05 V06 V07 V08 V09 V10 V11 V12 Avg. Std. DSC(%) RVD(%) HD(mm) ASD(mm) Our proposed method yields a mean DSC of 86.9%±3.2%, the RVD of 2.2%±13.9%, the HD of 7.2mm±1.3mm, and ASD of 1.5mm±0.2mm, which are satisfactory in our application.